Question:
Suppose from the estimation of a linear regression model \(Y_i=\beta_0+\beta_1X_i+e_i\) the residual sum of squares and the total sum of squares are obtained as 44 and 80, respectively. The value of coefficient of determination is ____________ (round off to two decimal places).
Suppose from the estimation of a linear regression model \(Y_i=\beta_0+\beta_1X_i+e_i\) the residual sum of squares and the total sum of squares are obtained as 44 and 80, respectively. The value of coefficient of determination is ____________ (round off to two decimal places).
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If you know TSS and RSS, then \(R^2\) is immediate via \(1-\text{RSS}/\text{TSS}\); no need to compute ESS separately.
Updated On: Sep 1, 2025
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Correct Answer: 0.43
Solution and Explanation
Step 1: Recall the definition.
Coefficient of determination \(R^2 = 1 - \dfrac{\text{RSS}}{\text{TSS}}\).
Step 2: Substitute the values.
\(R^2 = 1 - \dfrac{44}{80} = 1 - 0.55 = 0.45\).
Step 3: Round as asked.
Rounded to two decimals: \(\boxed{0.45}\).
Coefficient of determination \(R^2 = 1 - \dfrac{\text{RSS}}{\text{TSS}}\).
Step 2: Substitute the values.
\(R^2 = 1 - \dfrac{44}{80} = 1 - 0.55 = 0.45\).
Step 3: Round as asked.
Rounded to two decimals: \(\boxed{0.45}\).
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